Hospice Evaluation and Legitimate Payment Act of 2013 - Amends title XVIII (Medicare) of the Social Security Act with respect to the face-to-face encounter framework in hospice care. Allows a clinical nurse specialist, physician assistant, or other health professional (in addition to a hospice physician or a nurse practitioner, as under current law) to conduct the face-to-face encounter with the individual to determine continued eligibility for hospice care before the first 60-day (currently 180-day) recertification period and each subsequent recertification.

Directs the Secretary of Health and Human Services (HHS) to establish a Medicare Hospital Payment Reform demonstration program to test any revisions to the methodology for determining payment rates for routine home care and other hospice care services.

Sets at every three years the frequency of surveys of certified hospice programs.